Rectifier circuits & DC power supplies Goal: Generate the DC voltages – needed for most electronics – starting with the AC power that comes through the power line. ? 120 VRMS f = 60 Hz (T = 16.67 ms) =()sin How to take time-varying voltage with an average value of 0 and turn it into a DC voltage? EE 201 rectifiers – 1 120 VRMS transformer peak rectifier regulator DC load transformer : reduces AC amplitude to something safe and manageable. Vpeak from the transformer will be a few volts bigger than the desired DC voltage. peak rectifier : breaks up the AC waveform and produces a VDC ≈ Vpeak . regulator : Refines the output of the rectifier. (optional) Issues: • Total power • Efficiency • Cost • Load regulation (Does VDC change as the load draws different amounts of current?) • Line regulation (Does VDC change if the input AC amplitude changes?) EE 201 rectifiers – 2 Half-wave rectifier + Resistor represent a load. + ()= sin V v S – R We are trying to deliver Vp = 3 V. – DC power to the load. Diode is off until VS > 0.7 V. Current flows when diode is in forward conduction. The output tracks the input during positive half cycle. EE 201 rectifiers – 3 The diode turns off when VS < 0.7 V. It stays off during the negative half cycle of the sinusoid. . V > 0: () sin . () S ≈ − ≈ − VS < 0: v (t) = 0: R ≠ 0 ! To get the negative half of the cycle, turn the diode around. EE 201 rectifiers – 4 Time delay Note that since the diode will not turn on until the sinusoid goes above ≈ 0.7 V, there is time delay before the rectifier “turns on”. It is a simple matter to determine the delay time, using the “on-off” diode model: 3 VS Vo 2 . = sin 1 diode off again (V) output . o 0 follows , V input S = arcsin V -1 diode initially off -2 If f = 60 Hz (T = 16.67 ms) -3 and Vp = 3 V, t’ = 0.62 ms. time There is a similar time offset at the other end of the positive half cycle. The effect of the time offset become negligible if VP >> 0.7 V. EE 201 rectifiers – 5 Peak rectifier Add a largish capacitor after the diode, in parallel with the load. + i + iD C + C C + v V v VS – R S – R i i C R – iR – Initially, diode is on & cap charges While VS < vC , diode is off! to VP - 0.7 V. Cap discharges through load. EE 201 rectifiers – 6 + iD C + v VS – R iC iR – Diode stay off until VS comes back When VS falls to less than vC, the around and becomes bigger than diode turn off again, and the cycle vC. Then diode comes on again continues. and re-charges the capacitor. EE 201 rectifiers – 7 Not a a perfect DC voltage at output. There is some variation (ripple) around an average value. ()= . − ()=[ .]exp − − [ .]exp ≈ − − = () () 0 t1 − 0 T =[ .] exp − − − () () ≈ − t1 = time when diode conducts again. EE 201 t1 ≈ T rectifiers – 8 Example 1 + C = 100 µF + C =()sin V v S – o R = 5000 ! T = 16.67 ms – Find the average value of vo and the ripple voltage. Repeat for R = 1000 ! and 200 !. =[ .] exp − − − . =[ .] exp − − −()() = 0.47 V . ()= () = . = . − − R = 1 k! R = 200 ! Drawing more current causes the ripple to increase and VDC V = 2.19 V ripple Vripple = 8.09 V to droop. Can fight this with Vo (avg) = 13.2 V Vo (avg) = 10.2 V more capacitance. EE 201 rectifiers – 9 Example 2 + =()sin + C V v R = 1000 ! S – o T = 16.67 ms – Find the capacitance so that the ripple will be no bigger than 1 V. What is the DC voltage? =[ .] exp − − − − . − = ln = ln = 397 µF − − . − − . − ()= () = . = . − − What capacitance is needed to limit the ripple to 0.1 V? C = 4000 µF !!! EE 201 rectifiers – 10 Full-wave rectifier With a few more diodes, we can rectify the entire sinusoidal input. 1 4 1 + – v + 4 3 + R + V v VS S – R or – – 2 3 2 The diodes are in a bridge configuration. During the positive half cycle of the input, diodes 1 and 2 will be forward biased. Current will flow from the positive source through those diodes and the resistor to generate a positive voltage across the resistor. During the negative half cycle of the input, diodes 3 and 4 will be forward biased. Current will flow from the negative source through those diodes and the resistor to generate a positive voltage across the resistor, again. EE 201 rectifiers – 11 1 4 – v + – v + V + R V + R S – S – i i 2 R R 3 Note that there are no two diode drops in the conduction path(s). Also, the frequency is effectively doubled. EE 201 rectifiers – 12 Full-wave peak rectifier Placing a capacitor in parallel with the load, turns the circuit into a full- wave peak rectifier. It behaves essentially the same as the half-wave peak rectifier except with twice the frequency (half the period). ()= sin Vp = 8 V. 1 + C + 4 3 v VS – R R – 2 The ripple voltage is calculated in exactly the same way, except that the period is cut in half (frequency doubled). Same as doubling =[ .] exp − − − capacitance! EE 201 rectifiers – 13 Example 3 You want to use a wall transformer that produces 10-VRMS at the secondary to generate a DC voltage. The desired voltage DC should be greater than 12 V and it should be able to supply at least 50 mA while keeping the voltage ripple to less than 5%. Design the rectifier to meet these goals. (Note: f = 60 Hz.) 10 VRMS → 14.1 V amplitude effective RL ≈ Vo / Io = 12.0 V / (50 mA) = 240 ! Note: This would be the minimum value of effective resistance. If we choose C to meet the ripple requirement, then we will still be safe if we use a slightly higher Vo. Two options: half-wave or full-wave rectifier. Try both. Half-wave: Vo(max) = Vp – 0.7 V = 13.4 V → Vripple ≤ 0.67 V. − = ln − − . = 1350 µF − Vo(avg) = Vo(max) – Vripple / 2 = 13.06 V. EE 201 rectifiers – 14 Full-wave: Vo(max) = Vp – 2(0.7 V) = 12.74 V → Vripple ≤ 0.64 V. − = ln = µ − − () Vo(avg) = Vo(max) – Vripple / 2 = 12.42 V. Either approach will work and meet the requirements. The full-wave version uses extra diodes, but only half the capacitance. Since diodes are nearly free (pennies per piece), but big capacitors are relatively expensive, the full-wave circuit will actually cost less than the half-wave. This is why full-wave rectifiers are used more commonly than half-wave rectifiers. Component manufactures supply full-wave bridge rectifiers packaged as single unit with the transformer sinusoid as input the rectified waveform as the output. EE 201 rectifiers – 15.